%------------------------------------------------------------------------------
% File : E-SAT---3.5.1
% Problem : SET924+1 : TPTP v9.3.1. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% Computer : n003.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Thu Sep 24 02:18:54 PM UTC 2026
% Result : Theorem 0.12s 0.41s
% Output : CNFRefutation 0.12s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 2
% Syntax : Number of formulae : 14 ( 3 unt; 0 def)
% Number of atoms : 29 ( 14 equ)
% Maximal formula atoms : 4 ( 2 avg)
% Number of connectives : 30 ( 15 ~; 8 |; 2 &)
% ( 5 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 4 avg)
% Maximal term depth : 3 ( 2 avg)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 4 ( 4 usr; 2 con; 0-2 aty)
% Number of variables : 16 ( 0 sgn 12 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(t67_zfmisc_1,conjecture,
! [X1,X2] :
( set_difference(singleton(X1),X2) = singleton(X1)
<=> ~ in(X1,X2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t67_zfmisc_1) ).
fof(l34_zfmisc_1,axiom,
! [X1,X2] :
( set_difference(singleton(X1),X2) = singleton(X1)
<=> ~ in(X1,X2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',l34_zfmisc_1) ).
fof(c_0_2,negated_conjecture,
~ ! [X1,X2] :
( set_difference(singleton(X1),X2) = singleton(X1)
<=> ~ in(X1,X2) ),
inference(assume_negation,[status(cth)],[t67_zfmisc_1]) ).
fof(c_0_3,negated_conjecture,
~ ! [X1,X2] :
( set_difference(singleton(X1),X2) = singleton(X1)
<=> ~ in(X1,X2) ),
inference(fof_simplification,[status(thm)],[c_0_2]) ).
fof(c_0_4,plain,
! [X1,X2] :
( set_difference(singleton(X1),X2) = singleton(X1)
<=> ~ in(X1,X2) ),
inference(fof_simplification,[status(thm)],[l34_zfmisc_1]) ).
fof(c_0_5,negated_conjecture,
( ( ~ in(esk1_0,esk2_0)
| set_difference(singleton(esk1_0),esk2_0) = singleton(esk1_0) )
& ( in(esk1_0,esk2_0)
| set_difference(singleton(esk1_0),esk2_0) != singleton(esk1_0) ) ),
inference(fof_nnf,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_3])])])]) ).
fof(c_0_6,plain,
! [X7,X8] :
( ( set_difference(singleton(X7),X8) = singleton(X7)
| in(X7,X8) )
& ( ~ in(X7,X8)
| set_difference(singleton(X7),X8) != singleton(X7) ) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_4])])]) ).
cnf(c_0_7,negated_conjecture,
( set_difference(singleton(esk1_0),esk2_0) != singleton(esk1_0)
| in(esk1_0,esk2_0) ),
inference(split_conjunct,[status(thm)],[c_0_5]) ).
cnf(c_0_8,plain,
( set_difference(singleton(X1),X2) = singleton(X1)
| in(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_6]) ).
cnf(c_0_9,negated_conjecture,
( ~ in(esk1_0,esk2_0)
| set_difference(singleton(esk1_0),esk2_0) = singleton(esk1_0) ),
inference(split_conjunct,[status(thm)],[c_0_5]) ).
cnf(c_0_10,negated_conjecture,
in(esk1_0,esk2_0),
inference(csr,[status(thm)],[c_0_7,c_0_8]) ).
cnf(c_0_11,plain,
( ~ in(X1,X2)
| set_difference(singleton(X1),X2) != singleton(X1) ),
inference(split_conjunct,[status(thm)],[c_0_6]) ).
cnf(c_0_12,negated_conjecture,
set_difference(singleton(esk1_0),esk2_0) = singleton(esk1_0),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_9,c_0_10])]) ).
cnf(c_0_13,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_11,c_0_12]),c_0_10])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SET924+1 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.04 % Command : run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.08/0.35 % Computer : n003.cluster.edu
% 0.08/0.35 % Model : x86_64 x86_64
% 0.08/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.35 % Memory : 8046.5625MB
% 0.08/0.35 % OS : Linux 6.8.0-71-generic
% 0.08/0.35 % CPULimit : 300
% 0.08/0.35 % WCLimit : 300
% 0.08/0.35 % DateTime : Mon Sep 21 05:46:00 UTC 2026
% 0.08/0.35 % CPUTime :
% 0.08/0.35 Running run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.12/0.39 Running first-order theorem proving
% 0.12/0.39 Running: /export/starexec/sandbox2/solver/bin/eprover --delete-bad-limit=2000000000 --definitional-cnf=24 -s --print-statistics -R --print-version --proof-object --auto-schedule=8 --cpu-limit=300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.12/0.41 % Version: 3.5.1
% 0.12/0.41 % Preprocessing class: FSSSSMSSSSSNFFN.
% 0.12/0.41 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.12/0.41 % Starting G-E--_302_C18_F1_URBAN_RG_S04BN with 1500s (5) cores
% 0.12/0.41 % Starting new_bool_3 with 300s (1) cores
% 0.12/0.41 % Starting new_bool_1 with 300s (1) cores
% 0.12/0.41 % Starting sh5l with 300s (1) cores
% 0.12/0.41 % sh5l with pid 3533727 completed with status 0
% 0.12/0.41 % Result found by sh5l
% 0.12/0.41 % Preprocessing class: FSSSSMSSSSSNFFN.
% 0.12/0.41 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.12/0.41 % Starting G-E--_302_C18_F1_URBAN_RG_S04BN with 1500s (5) cores
% 0.12/0.41 % Starting new_bool_3 with 300s (1) cores
% 0.12/0.41 % Starting new_bool_1 with 300s (1) cores
% 0.12/0.41 % Starting sh5l with 300s (1) cores
% 0.12/0.41 % (lift_lambdas = 0, lambda_to_forall = 0,unroll_only_formulas = 0, sine = gf500_gu_R04_F100_L20000)
% 0.12/0.41 % SinE strategy is gf500_gu_R04_F100_L20000
% 0.12/0.41 % Search class: FGHSF-FFSF21-SFFFFFNN
% 0.12/0.41 % Scheduled 5 strats onto 1 cores with 300 seconds (300 total)
% 0.12/0.41 % Starting SubtermCWHack with 31s (1) cores
% 0.12/0.41 % SubtermCWHack with pid 3533730 completed with status 0
% 0.12/0.41 % Result found by SubtermCWHack
% 0.12/0.41 % Preprocessing class: FSSSSMSSSSSNFFN.
% 0.12/0.41 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.12/0.41 % Starting G-E--_302_C18_F1_URBAN_RG_S04BN with 1500s (5) cores
% 0.12/0.41 % Starting new_bool_3 with 300s (1) cores
% 0.12/0.41 % Starting new_bool_1 with 300s (1) cores
% 0.12/0.41 % Starting sh5l with 300s (1) cores
% 0.12/0.41 % (lift_lambdas = 0, lambda_to_forall = 0,unroll_only_formulas = 0, sine = gf500_gu_R04_F100_L20000)
% 0.12/0.41 % SinE strategy is gf500_gu_R04_F100_L20000
% 0.12/0.41 % Search class: FGHSF-FFSF21-SFFFFFNN
% 0.12/0.41 % Scheduled 5 strats onto 1 cores with 300 seconds (300 total)
% 0.12/0.41 % Starting SubtermCWHack with 31s (1) cores
% 0.12/0.41 % Preprocessing time : 0.001 s
% 0.12/0.41
% 0.12/0.41 % Proof found!
% 0.12/0.41 % SZS status Theorem
% 0.12/0.41 % SZS output start CNFRefutation
% See solution above
% 0.12/0.41 % Parsed axioms : 5
% 0.12/0.41 % Removed by relevancy pruning/SinE : 2
% 0.12/0.41 % Initial clauses : 5
% 0.12/0.41 % Removed in clause preprocessing : 0
% 0.12/0.41 % Initial clauses in saturation : 5
% 0.12/0.41 % Processed clauses : 7
% 0.12/0.41 % ...of these trivial : 0
% 0.12/0.41 % ...subsumed : 0
% 0.12/0.41 % ...remaining for further processing : 7
% 0.12/0.41 % Other redundant clauses eliminated : 0
% 0.12/0.41 % Clauses deleted for lack of memory : 0
% 0.12/0.41 % Backward-subsumed : 0
% 0.12/0.41 % Backward-rewritten : 1
% 0.12/0.41 % Generated clauses : 3
% 0.12/0.41 % ...of the previous two non-redundant : 2
% 0.12/0.41 % ...aggressively subsumed : 0
% 0.12/0.41 % Contextual simplify-reflections : 1
% 0.12/0.41 % Paramodulations : 3
% 0.12/0.41 % Factorizations : 0
% 0.12/0.41 % NegExts : 0
% 0.12/0.41 % Equation resolutions : 0
% 0.12/0.41 % Disequality decompositions : 0
% 0.12/0.41 % Total rewrite steps : 2
% 0.12/0.41 % ...of those cached : 1
% 0.12/0.41 % Propositional unsat checks : 0
% 0.12/0.41 % Propositional check models : 0
% 0.12/0.41 % Propositional check unsatisfiable : 0
% 0.12/0.41 % Propositional clauses : 0
% 0.12/0.41 % Propositional clauses after purity: 0
% 0.12/0.41 % Propositional unsat core size : 0
% 0.12/0.41 % Propositional preprocessing time : 0.000
% 0.12/0.41 % Propositional encoding time : 0.000
% 0.12/0.41 % Propositional solver time : 0.000
% 0.12/0.41 % Success case prop preproc time : 0.000
% 0.12/0.41 % Success case prop encoding time : 0.000
% 0.12/0.41 % Success case prop solver time : 0.000
% 0.12/0.41 % Current number of processed clauses : 6
% 0.12/0.41 % Positive orientable unit clauses : 2
% 0.12/0.41 % Positive unorientable unit clauses: 0
% 0.12/0.41 % Negative unit clauses : 1
% 0.12/0.41 % Non-unit-clauses : 3
% 0.12/0.41 % Current number of unprocessed clauses: 0
% 0.12/0.41 % ...number of literals in the above : 0
% 0.12/0.41 % Current number of archived formulas : 0
% 0.12/0.41 % Current number of archived clauses : 1
% 0.12/0.41 % Clause-clause subsumption calls (NU) : 1
% 0.12/0.41 % Rec. Clause-clause subsumption calls : 1
% 0.12/0.41 % Non-unit clause-clause subsumptions : 1
% 0.12/0.41 % Unit Clause-clause subsumption calls : 0
% 0.12/0.41 % Rewrite failures with RHS unbound : 0
% 0.12/0.41 % BW rewrite match attempts : 1
% 0.12/0.41 % BW rewrite match successes : 1
% 0.12/0.41 % Condensation attempts : 0
% 0.12/0.41 % Condensation successes : 0
% 0.12/0.41 % Termbank termtop insertions : 417
% 0.12/0.41 % Search garbage collected termcells : 76
% 0.12/0.41
% 0.12/0.41 % -------------------------------------------------
% 0.12/0.41 % User time : 0.002 s
% 0.12/0.41 % System time : 0.001 s
% 0.12/0.41 % Total time : 0.004 s
% 0.12/0.41 % Maximum resident set size: 3628 pages
% 0.12/0.41
% 0.12/0.41 % -------------------------------------------------
% 0.12/0.41 % User time : 0.003 s
% 0.12/0.41 % System time : 0.007 s
% 0.12/0.41 % Total time : 0.009 s
% 0.12/0.41 % Maximum resident set size: 4608 pages
% 0.12/0.41 % E exiting
%------------------------------------------------------------------------------